U.S. patent application number 14/356331 was filed with the patent office on 2014-10-30 for method for simulating rubber material.
The applicant listed for this patent is Sumitomo Rubber Industries Ltd.. Invention is credited to Hiroyuki Kishimoto, Masato Naito.
Application Number | 20140324401 14/356331 |
Document ID | / |
Family ID | 48429428 |
Filed Date | 2014-10-30 |
United States Patent
Application |
20140324401 |
Kind Code |
A1 |
Kishimoto; Hiroyuki ; et
al. |
October 30, 2014 |
METHOD FOR SIMULATING RUBBER MATERIAL
Abstract
Provided is a method that is useful for accurately setting a
rubber material model for a simulation from an actual rubber
material and obtaining a high-accuracy calculation result. A method
for simulating a rubber material containing a filler comprises a
measurement step (S1) for measuring scattering data relating to
x-rays and/or neutron in the rubber material, a visualization step
(S2) for specifying the three-dimensional structure of the filler
in the rubber material through a reverse Monte Carlo method from
the scattering data, model setting steps (S3 to S6) for setting a
rubber material model on the basis of the three-dimensional
structure of the filler, and a step for performing a deformation
simulation on the basis of the rubber material model, wherein in
the measurement step, obtaining the scattering data with a
scattering vector (q) within the range of 10.sup.-4 nm.sup.-1 to 10
nm.sup.-1.
Inventors: |
Kishimoto; Hiroyuki;
(Kobe-shi, JP) ; Naito; Masato; (Kobe-shi,
JP) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Sumitomo Rubber Industries Ltd. |
Kobe-shi, Hyogo |
|
JP |
|
|
Family ID: |
48429428 |
Appl. No.: |
14/356331 |
Filed: |
October 29, 2012 |
PCT Filed: |
October 29, 2012 |
PCT NO: |
PCT/JP2012/077888 |
371 Date: |
May 5, 2014 |
Current U.S.
Class: |
703/2 |
Current CPC
Class: |
G06F 30/20 20200101;
G01N 33/445 20130101; G01N 23/201 20130101; G06F 30/23 20200101;
G01N 23/207 20130101; C08L 21/00 20130101 |
Class at
Publication: |
703/2 |
International
Class: |
G06F 17/50 20060101
G06F017/50 |
Foreign Application Data
Date |
Code |
Application Number |
Nov 18, 2011 |
JP |
2011-252984 |
Claims
1. A method for simulating a rubber material containing a filler,
the method comprising: a measuring step of measuring scattering
data of an X-ray and/or a neutron of the rubber material; a
visualization step of determining a three-dimensional structure of
the filler in the rubber material with reverse Monte Carlo method
by using the scattering data; a model setting step of setting a
rubber material model based on the three-dimensional structure of
the filler; and a step of performing a deformation simulation based
on the rubber material mode, wherein the measuring step includes
obtaining scattering data in a range in which a scattering vector
(q) expressed by equation (1) is greater than 10.sup.-4 nm.sup.-1
and less than 10 nm.sup.-1, q=4.pi.sin .theta./.lamda. (1), wherein
.lamda., is a wavelength of an electromagnetic wave or particle
beam, and .theta. is a half of a scattering angle.
2. The method for simulating a rubber material according to claim
1, wherein in the measuring step, a beam size of the X-ray and/or
neutron entering a sample is equal to or more than 60 .mu.m and
equal to or less than 30 mm.
3. The method for simulating a rubber material according to claim
1, wherein in the measuring step, incident X-ray intensity to be
measured with an X-ray scattering method is equal to or more than
10.sup.10 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw) and equal to or
less than 10.sup.23 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw).
4. The method for simulating a rubber material according to claim
2, wherein in the measuring step, incident X-ray intensity to be
measured with an X-ray scattering method is equal to or more than
10.sup.10 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw) and equal to or
less than 10.sup.23 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw).
Description
TECHNICAL FIELD
[0001] The present invention relates to a method for simulating a
rubber material, and in particular, relates to a method including
accurately setting a rubber material model for a simulation from an
actual rubber material so as to be useful for obtaining an accurate
computational result.
BACKGROUND ART
[0002] From the viewpoint of reinforcement, fillers, such as carbon
black, and silica, are blended in a rubber material for tires or
the like. It has been roughly found that dispersibility of the
fillers in the rubber material considerably affects rubber strength
or the like. However, the details thereof are not made so clear. It
is therefore important to accurately observe a three-dimensional
dispersed state (aggregated structure) of the fillers in the rubber
material so as to perform a simulation using a model based on the
dispersed state.
[0003] With the recent technological developments, it has been
proposed to obtain an electron beam transmitted image of the rubber
material with a 3D-TEM (transmission electron microscope), and then
configure a three-dimensional structure of the rubber material from
the image with tomography method so as to set a rubber material
model based on the three-dimensional structure.
[0004] Unfortunately, all information obtainable with the 3D-TEM
are structure information about a local portion among the entirety
of rubber, and hence there is the problem that statistical
properties are poor for performing the simulation. This leads to
deterioration of the accuracy of the simulation.
DISCLOSURE OF THE INVENTION
Problems to be Solved by the Invention
[0005] The present invention has been made in view of the foregoing
problem, and has an object to provide a method for simulating a
rubber material capable of solving the above problem. The method
basically includes determining a three-dimensional structure of the
rubber material having high statistical properties with reverse
Monte Carlo method by using scattering data in a specific
scattering vector range obtained using an x-ray and/or neutron of
the rubber material, and setting a rubber material model based on
the three-dimensional structure.
Means of Solving the Problems
[0006] The present invention is a method for simulating a rubber
material containing fillers. The method includes a measuring step
of measuring scattering data of an x-ray and/or neutron of the
rubber material, a visualization step of determining a
three-dimensional structure of the fillers in the rubber material
with reverse Monte Carlo method by using the scattering data, a
model setting step of setting a rubber material model based on the
three-dimensional structure of the fillers, and a step of
performing a deformation simulation based on the rubber material
model. The measuring step includes obtaining scattering data in a
range in which a scattering vector (q) expressed by equation (1) is
greater than 10.sup.-4 nm.sup.-1 and less than 10 nm.sup.-1,
q=4.pi.sin .theta./.lamda. . . . (1), wherein .lamda. is a
wavelength of an electromagnetic wave or particle beam, and .theta.
is a half of a scattering angle.
[0007] In the measuring step, a beam size of an x-ray and/or
neutron ray entering a sample is preferably equal to or more than
60 .mu.m and equal to or less than 30 mm.
[0008] In the measuring step, incident x-ray intensity to be
measured with an x-ray scattering method is equal to or more than
10.sup.10 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw) and equal to or
less than 10.sup.23 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw).
Effects of the Invention
[0009] The method for simulating a rubber material according to the
present invention includes the measuring step of measuring
scattering data of the x-ray and/or neutron of the rubber material,
the visualization step of determining a three-dimensional structure
of fillers in the rubber material with the reverse Monte Carlo
method by using the scattering data, the model setting step of
setting a rubber material model based on the three-dimensional
structure of the fillers, and the step of performing a deformation
simulation based on the rubber material model. The measuring step
includes obtaining scattering data in the range in which the
scattering vector (q) expressed by the following equation is
greater than 10.sup.-4 nm.sup.-1 and less than 10 nm.sup.-1,
q=4.pi.sin .theta./.lamda., wherein .lamda. is a wavelength of an
electromagnetic wave or particle beam, and .theta. is a half of a
scattering angle.
[0010] In general, the fillers (reinforced fillers), such as
silica, for use in rubber have a primary particle size of
approximately 10 to 100 nm. A primary aggregated body that a
plurality of particles of the fillers aggregate generally has a
size of approximately 500 nm or less. On the other hand, the
scattering vector relates to space dissolution obtained by a
computation with the reverse Monte Carlo method. Therefore, in the
case of using a large scattering vector relative to the primary
particle size of the fillers or the size of the primary aggregated
body thereof, this case leads to a computation with unnecessary
space dissolution, resulting in poor efficiency. Reversely, in the
case of using a small scattering vector, though this case allows
observation even with a scanning electron microscope (SEM) and an
optical microscope, this case is not practical because much
computation costs are required. With the present invention, the
scattering vector (q) is limited to the above-mentioned range,
thereby ensuring efficient and accurate determination of the shape
of the primary aggregated body and the layout of the primary
particles in the fillers.
[0011] Hence, according to the foregoing steps, it is ensured to
accurately determine a three-dimensional structure that the actual
rubber material actually has, thereby obtaining a more accurate
rubber material model based on the three-dimensional structure.
Thus, the present invention ensures an accurate simulation
result.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] FIG. 1 is a schematic partially enlarged cross-sectional
view of a rubber material according to an embodiment of the present
invention.
[0013] FIG. 2 is a flow chart describing the procedure according to
the embodiment.
[0014] FIG. 3 is a three-dimensional image of the rubber material
obtained from a sample with a method according to the
embodiment.
[0015] FIG. 4(a) is a partially enlarged view of a two-dimensional
rubber material model; FIG. 4(b) is an enlarged view of a main part
thereof.
[0016] FIG. 5(a) is a partially enlarged view of another
two-dimensional rubber material model; FIG. 5(b) is an enlarged
view of a main part thereof.
[0017] FIG. 6 is a schematic enlarged view of a part of a
three-dimensional rubber material model.
[0018] FIG. 7 is an enlarged view of a cubic element describing
subdivision of the cubic element.
MODE FOR CARRYING OUT THE INVENTION
[0019] An embodiment of the present invention will be described
below with reference to the drawings. In the present embodiment, as
shown in FIG. 1, an analysis object is a rubber material (c) with
fillers containing rubber ingredients (a) as matrix rubber, and
silica as fillers (b). A deformation computation of the rubber
material (c) is simulated with a computer (not shown).
[0020] Examples of the rubber ingredients (a) include natural
rubber (NR), isoprene rubber (IR), butyl rubber (IIR), butadiene
rubber (BR), styrene butadiene rubber (SBR), styrene isoprene
butadiene rubber (SIBR), ethylene propylene diene rubber (EPDM),
chloroprene rubber (CR), and acrylonitrile butadiene rubber
(NBR).
[0021] Examples of the fillers (b) include, without limitation to
silica, carbon black, clay, talc, magnesium carbonate, and
magnesium hydroxide. The rubber material (c) may be suitably
blended with various materials generally used in rubber industry,
such as sulfur, and vulcanization accelerator.
[0022] FIG. 2 shows a flow chart for performing a simulation method
of the present embodiment. In the present embodiment, firstly, a
measuring step of measuring scattering data of an x-ray and/or
neutron of the rubber material (c) is performed (step S1).
[0023] The measuring step is performed with, for example, small
angle scattering method. With the small angle scattering method,
the x-ray or neutron is irradiated to the rubber material. An
incident x-ray reflects information about an electron density
distribution within material (the distribution of the fillers in
the present embodiment), and a scattering x-ray (or scattering
neutron) occurs around the incident x-ray (or the neutron ray).
That is, in the presence of a non-uniform region of particles and
density in the rubber material, scattering occurs around the
incident x-ray irrespective of whether crystalline or amorphous.
The scattering x-ray exposes, for example, a detector so as to form
an x-ray latent image corresponding to the scattering data in the
interior of the detector. The x-ray latent image is visualized to
obtain three-dimensional structure information about the
fillers.
[0024] The measuring step is performed in a radiation light
research facility, such as SPring-8, and PF. In the present
embodiment, the measurement was made with the small angle x-ray
scattering method using two kinds of beamlines of BL20XU and BL4082
in the SPring-8. As the detector, an x-ray image intensifier plus a
CCD detector (produced by Hamamatsu Photonics K.K.), and a
solid-state semiconductor detector PILATUS 100K (produced by
DECTRIS Ltd.) were used. The use of these two beamlines ensures
obtaining scattering data in the range in which the scattering
vector expressed by the following equation (1) is greater than
10.sup.-3 nm.sup.-1 and less than 10 nm.sup.-1. With the present
embodiment, two-dimensional small-angle x-ray scattering data in
the range of 1.2.times.10.sup.-3 nm.sup.-1<q<2 nm.sup.-1 with
respect to a scattering vector (q) were obtained.
q=4.pi.sin .theta./.lamda. (1),
wherein .lamda. is a wavelength of an electromagnetic wave or
particle beam, and .theta. is a half of a scattering angle.
[0025] The fillers (reinforced fillers) for use in rubber
preferably have a primary particle size of approximately 10 to 100
nm. A primary aggregated body that a plurality of particles of the
fillers aggregate preferably generally has a size of approximately
500 nm or less. On the other hand, the scattering vector (q)
relates to space dissolution obtained from a computation with the
reverse Monte Carlo method. Therefore, in the case of using a large
scattering vector relative to the primary particle size of the
fillers or the size of the primary aggregated body thereof, this
case leads to a computation with unnecessary space dissolution,
resulting in poor efficiency. Reversely, in the case of using a
small scattering vector, though this case allows observation even
with a scanning electron microscope (SEM) and an optical
microscope, this case is not practical because much computation
costs are required. With the present embodiment, the range of the
scattering vector (q) is limited to the above-mentioned range,
thereby producing the advantage of ensuring efficient and accurate
determination of the shape of the primary aggregated body and the
layout of the primary particles. The range of the scattering vector
(q) is more preferably 10.sup.-4 nm.sup.-1<q<1 nm.sup.-1, and
still more preferably 10.sup.-3 nm.sup.-1<q<0.7
nm.sup.-1.
[0026] In the measuring step, the beam size of an x-ray and/or
neutron ray entering a rubber material (sample) is preferably in
the range of 60 .mu.m or more and 30 mm or less. As structure
information obtained from the scattering of the x-ray or neutron
ray, average information in the beam size of the x-ray or neutron
entered the sample are obtainable, thus ensuring data having a
higher statistic than a 3D-TEM.
[0027] In the reverse Monte Carlo method (described later), the
beam size of 60 .mu.m or more is preferably irradiated to the
sample in order to compute scattering data of the scattering vector
(q) of 10.sup.-4 nm.sup.1<q<10 nm.sup.-1. When the beam size
is less than 60 .mu.m, the statistic of the scattering data is
small relative to a desired structure size, resulting in a risk of
failing to accurately determine a space layout of the fillers.
Further, in the case of using a synchrotron radiation x-ray as an
incident x-ray light source, the employment of the beam size of
less than 60 .mu.m causes a speckle-shaped scattering pattern due
to the influence of x-ray space coherence. The speckle-shaped
scattering pattern constitutes a noise composition, thus being
unsuitable for performing the reverse Monte Carlo method. On the
other hand, when the beam size is greater than 30 mm, it is
difficult to form an optimum optical system, resulting in a risk of
smearing (image blur) of a scattering pattern.
[0028] In the measuring step, incident x-ray intensity measured
with x-ray scattering method is preferably in the range of
10.sup.10 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw) or more and
10.sup.23 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw) or less. Incident
x-ray brightness considerably relates to an S/N ratio of the X-ray
scattering data. When the incident X-ray brightness is less than
10.sup.10 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw), there is a
tendency that signal intensity is weaker than a statistical error
in the x-ray. It is difficult to obtain data of a sufficiently
satisfactory S/N ratio even with a longer measuring time. On the
other hand, when the incident x-ray brightness is more than
10.sup.23 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw), there is a risk
that the sample is subjected to radiation damage, failing to make
the measurement. In view of the foregoing, the incident x-ray
intensity is more preferably 10.sup.21
(photons/s/mrad.sup.2/mm.sup.2/0.1% bw) or less, and still more
preferably 10.sup.20 (photons/s/mrad.sup.2/mm.sup.2/0.1% bw) or
less.
[0029] Subsequently, with the present embodiment, a visualization
step of determining a three-dimensional structure of the fillers in
the rubber material with the reverse Monte Carlo method by using
the scattering data obtained in the measuring step is performed
(step S2).
[0030] The reverse Monte Carlo method is the method whose study has
been advanced as a technique for determining the atomic and
molecular structures of an amorphous material, such as liquid
metal. In general, scattering intensity I(q) obtained from the
x-ray and/or neutron ray is expressed by the following equation
(2).
I(q)=S(q)F(q) (2)
[0031] Here, F(q) is a function indicating the shape of a
scattering body in a material. In the present embodiment, the
primary particles of the fillers in the rubber are denoted by F(q).
When F(q) is a shape factor of the primary particles of the
fillers, S(q) becomes one related to the space layout of the
primary particles. Here, a scattering factor for a sphere is used
as the F(q). The scattering factor is expressed by the following
equation (3). In the equation (3), R is a radius of a sphere,
.DELTA..rho. is an electron density difference, v is a volume of
the sphere, and (q) is a scattering vector.
[ Equation 1 ] F ( q ) = ( .DELTA..rho. V ) 2 ( 3 sin ( qR ) - qR
cos ( qR ) ) 2 ( qR ) 6 ( 3 ) ##EQU00001##
[0032] With the technique of the reverse Monte Carlo method, a
plurality of particles are subjected to an initial arrangement in a
computer, and a computation is repeated while changing the
arrangement of the particles by using random numbers or the like
until an S.sub.cal (q) computationally obtained from Fourier
transformation of the initial arrangement coincides with an actual
measurement S.sub.exp (q). Actually, a structure is determined by
repeating the computation until the computation of x.sup.2 shown in
equation (4) converges. In the equation (4), .sigma..sup.2.sub.std
is a standard deviation.
[ Equation 2 ] .chi. 2 = q ( S exp ( q ) - S cal ( q ) ) 2 .sigma.
std 2 ( 4 ) ##EQU00002##
[0033] FIG. 3 shows a three-dimensional structure of the fillers in
the rubber determined with the reverse Monte Carlo method described
above. The three-dimensional structure is stored on the computer as
numeric data.
[0034] Subsequently, with the present embodiment, the step of
obtaining a slice image of the rubber material (c) from the
three-dimensional structure is performed (step S3). The slice image
can easily be output from the computer by designating a
cross-sectional position because the three-dimensional structure
related to the fillers in the rubber material (c) has already been
obtained.
[0035] Subsequently, with the present embodiment, the step of
setting an initial rubber material model from the slice image of
the rubber material (c) is performed (step S4). This step includes
dividing the entire region of the slice image into at least two of
the rubber ingredients and the fillers by performing an image
processing of the slice image. This type of image processing is
already well known. The computer automatically classifies
individual regions of the slice image into a rubber part and a
filler part by previously setting a threshold value to information,
such as lightness and brightness of the image.
[0036] Then, after the slice image is classified into the rubber
part and the filler part by the image processing, an initial rubber
material model is set by dividing the slice image by basic elements
of identical shape respectively defined by ordered grids.
[0037] FIG. 4(a) shows a visualized part of an initial rubber
material model 5a of the present embodiment. FIG. 4(b) shows a
partially enlarged view thereof. The ordered grids are made of
grids GD defined by vertical lines L1 and lateral lines L2 arranged
at an identical pitch P on the x-axis and y-axis as shown in
enlarged dimension in FIG. 4(b). Squares defined by the vertical
lines L1 and the lateral lines L2 respectively constitute
individual basic elements (eb). More specifically, each of the
basic elements (eb) is a square element (rectangular element) whose
four corners correspond to nodes (n) arranged at individual
intersections of the vertical lines L1 and the lateral lines
L2.
[0038] The initial rubber material model 5a of the present
embodiment includes rubber models 21 resembling the rubber
ingredients (a), and filler models 22 resembling the fillers
(b).
[0039] The filler models 22 are colored and shown in FIG. 4(a) in
an easy-to-understand manner. The filler models 22 are set by
discretization of the fillers (b) using a finite number of basic
elements (eb).
[0040] The rubber models 21 are set by discretization of the rubber
ingredients (a) of the rubber material (c) using the finite number
of basic elements (eb).
[0041] In the foregoing element division, for example, using the
computer, the ordered grids are set on the slice image after
subjected to the image processing, and a computation is performed
for each of the basic elements (eb) as to whether the rubber
ingredients (a) or the fillers (b) occupies a larger area. Then, a
determination whether the individual elements (eb) belong to the
rubber model 21 or the filler model 22 is made based on
computational results. Thus, an initial analysis model can be
created in a short time by using only the basic elements (eb)
defined by the ordered grids. The initial analysis model is also
set as one that extremely resembles an analysis object owing to the
use of the accurately taken slice image of the three-dimensional
structure of the rubber material 5.
[0042] Information necessary for a numerical analysis owing to a
simulation are defined on the basic elements (eb). The numerical
analysis denotes, for example, a numerical analysis method, such as
finite element method. The information necessary for the analysis
include at least the numbers of the nodes (n) constituting the
individual basic elements (eb), and coordinate values of the nodes
(n). Further, a material property (physical property value) or the
like of a portion represented by each of the basic elements (eb) is
defined on the basic elements (eb). That is, a material constant
according to the physical properties of the fillers and the rubber
is defined on each of the basic elements (eb) of the rubber models
21 and the filler models 22. Then, all these pieces of information
are input into and stored in the computer.
[0043] Subsequently, with the present embodiment, a subdivision
region 23 to further divide the basic elements (eb) is set in a
part of the initial rubber material model 5a (step S5).
[0044] The subdivision region 23 is the portion of the rubber
material model 5a that is made of elements smaller than the basic
elements (eb). Therefore, the subdivision region 23 ensures a more
detailed investigation of deformation behavior thereof, and also
ensures high computational accuracy. Hence, the subdivision region
23 is preferably set to the portion that meets these
requirements.
[0045] In the case of the rubber material (c) blended with the
fillers, the rubber part (al) between the fillers (b) and (b)
adjacent to each other is susceptible to large strain and stress as
shown in FIG. 1. Therefore, with the present embodiment, the rubber
part disposed between the filler models 22 and 22 is set as the
subdivision region 23 so as to at least partially include the
rubber part (al).
[0046] The range of the subdivision region 23 may be designated by
a user with input means, such as a keyboard, and a mouse. Then,
predetermined information are added to the elements in a region
designated as the subdivision region 23, and the results are input
into the computer.
[0047] The subdivision region 23 may be determined with a different
method. For example, first, a deformation simulation is performed
using the initial rubber material model 5a and based on a
predetermined deformation condition. From the result of the
deformation simulation, a large deformation region including a
portion of the initial rubber material model 5a subjected to the
maximum stress or strain may be determined, and a region at least
partially including the large deformation region may be determined
as the subdivision region 23.
[0048] Subsequently, with the present embodiment, subdivision for
dividing individual basic elements of the subdivision region 5 into
two or more is performed (step S6).
[0049] The step S6 for the subdivision is performable by, for
example, reducing the pitch P of the vertical lines L1 and/or the
lateral lines L2 corresponding to the ordered grids passing through
the subdivision region 23 so as to reduce the basic elements (eb).
With the present embodiment, only the pitch of the lateral lines L2
defining the ordered grids and passing through the subdivision
region 23 is reduced to half of the pitch P that has been
determined for the initial rubber material model 5a, as shown in
FIG. 5(a) and FIG. 5(b), which is a partially enlarged view
thereof. Consequently, the basic elements (eb) of the rubber part
disposed between the filler models 22 and 22 are respectively
divided into two equal parts in the y-direction. That is, the
individual basic elements (eb) of the subdivision region 23 are
respectively divided into rectangular small elements (es) having an
identical x-dimension and a half y-dimension when compared with the
original basic elements (eb).
[0050] Accordingly, by performing the deformation simulation using
the analysis model 5b after subjected to the step S6 for the
subdivision, it is ensured to enhance the computational accuracy of
the rubber part between the filler models 22 and 22 (the
subdivision region 23), and it is also ensured to investigate in
detail of the deformation behavior of the rubber part. The change
of the pitch when performing the subdivision is not limited to the
reduction by half, but the pitch is settable to different values.
The step S3 for the subdivision may be repeated a plurality of
times until obtaining a necessary element resolution.
[0051] Although the foregoing embodiment has illustrated and
described the two-dimensional rubber material model 5a, the present
invention is of course applicable to a three-dimensional rubber
material model 5c with a similar procedure as shown in FIG. 6. In
this case, modeling is performable directly from the
three-dimensional structure of the rubber material (c) without
using the slice image. In the case of the three-dimensional model
5c, the basic elements (eb) defined by the ordered grids are
respectively made of a rectangular parallelepiped element.
[0052] For example, in the step of subdividing the
three-dimensional rubber material model 5c, a cubic small element
(es) that has a similar shape to the basic element (eb) and is
smaller than the basic element (eb) is set in the interior of the
basic element (eb) made of a cube so that their respective centers
of gravity coincide with each other as shown in the upper diagram
in FIG. 7. Then, individual nodes (ns) of the small elements (eb)
are respectively coupled to nodes (nb) of the basic element (eb)
via a side (s) as shown in the lower diagram in FIG. 7.
Consequently, the basic element (eb) can be divided into the single
cubic small element (es) and six hexahedral elements (ea)
surrounding the small element (es).
[0053] While the present invention has been described in detail,
the present invention is not limited to the foregoing embodiment,
but can be of course modified and carried out in various aspects.
For example, a similar measuring step can be performed with the
neutron ray instead of the x-ray.
Examples
[0054] The following test was conducted to confirm the effect of
the present invention. However, the present invention is not
limited to the following examples.
[0055] Various kinds of chemicals and devices used in the test are
as follows. That is, according to the following blending, materials
other than sulfur and vulcanization accelerator were mixed with a
Banbury mixer for four minutes under the condition that discharge
temperature was 160.degree. C., thereby obtaining a mixture. Then,
sulfur and vulcanization accelerator were added to the obtained
mixture. This was kneaded with an open role for two minutes under
the condition of 100.degree. C., thereby obtaining an unvulcanized
rubber composition. The obtained unvulcanized rubber composition
was vulcanized for 30 minutes at 175.degree. C., thereby obtaining
a vulcanized rubber.
TABLE-US-00001 TABLE 1 Comparative Comparative Comparative Example
1 Example 2 Example 3 Example 1 Example 2 Example 3 (Simulation
(Simulation (Simulation (Simulation (Simulation (Simulation Result)
Result) Resut) Result) Result) Result) Range of q(nm.sup.-1)
10.sup.-3 to 1 10.sup.-3 to 1 10.sup.-3 to 1 10 to 20 7 .times.
10.sup.-5 to 10.sup.-4 -- Used for Reverse Monte Carlo method
Incident X-ray about 10.sup.19 about 10.sup.19 about 10.sup.9 about
10.sup.19 about 10.sup.19 -- Intensity (photons/s/mra
d.sup.2/mm.sup.2/0.1% bw) Beam Size 500 5 500 500 100 -- Diameter
(.mu.m) Computational Possible Possible Possible Possible Possible
-- Possibility for X-ray Scattering Computational Possible Possible
Possible Impossible Impossible -- Possibility with Reverse Monte
Carlo Method Simulation 98 93 94 Not Performed Not Performed 100
Result [10% Modulus (index)]
[Chemicals]
[0056] SBR: "SBR1502" produced by Sumitomo Chemical Co., Ltd.
[0057] Silica: "115Gr" produced by RHODIA JAPAN LTD.
[0058] Silane Coupling agent: "Si69" produced by Degussa AG
[0059] Sulfur: Powder Sulfur produced by TSURUMI CHEMICAL INDUSTRY
CO., LTD.
[0060] Vulcanization accelerator A: "Nocceler NS" produced by OUCHI
SHINKO CHEMICAL INDUSTRIAL CO., LTD.
[0061] Then, a 1-mm-thick slab sheet was cut out of the vulcanized
rubber as a sample. When the sample has a thickness greater than 1
mm, there is a risk that multiple scattering occurs within the
rubber material, failing to make an accurate measurement.
[0062] Subsequently, a scattering data measurement for the obtained
sample was made with the small angle x-ray scattering method
according to the specification presented in Table 1 by using
beamlines of BL20XU and BL40B2 in the SPring-8. As detectors, the
x-ray image intensifier plus the CCD detector (produced by
Hamamatsu Photonics K.K.), and the solid-state semiconductor
detector "PILATUS 100K" (produced by DECTRIS Ltd.) were used as
described above. Scattering data in the range greater than
10.sup.-4 nm.sup.-1 and less than 1 nm.sup.-1 were obtained by
using the foregoing two beamlines. The three-dimensional structure
of silica was determined from the obtained scattering data with the
reverse Monte Carlo method. Based on the three-dimensional
structure of silica, a rubber material model, whose one side was
700 nm, was set, and a deformation simulation in which the model
was subjected to a 100% pull with finite element method was
performed. Then, a 100% modulus of the rubber material was computed
as an evaluation. For comparison, an actual vulcanized rubber was
also subjected to a 10% modulus pull test under the same condition
(comparative examples). The test results and the like are presented
in Table 1. The values of the 10% modulus in Table 1 are ones
obtained when the comparative examples are taken as 100, in which
value closer to 100 indicates being closer to the actual
measurement.
TABLE-US-00002 [Rubber Blending] (unit: parts by mass) SBR 100
Silica 50 Silane Coupling Agent 4 Sulfur 2 Vulcanization
Accelerator A 1
[0063] These examples have high correlation with the actual
vulcanized rubber. In contrast, comparative example 1, which
employed the scattering vector (q) smaller than the particle size
of silica, failed to obtain a convergent solution in the
computation with the reverse Monte Carlo method. In comparative
example 2, the scattering vector (q) fell within the range smaller
than the range of the present invention, and hence the computation
scale was too large to perform the computation with the reverse
Monte Carlo method.
DESCRIPTION OF THE REFERENCE NUMERAL
[0064] 5a, 5b, 5c Rubber material models [0065] 21 Rubber model
[0066] 22 Filler model
* * * * *